Sin licenses revisited

We analyse attempts to implement personalised regulation in the form of sin licenses (O'Donoghue and Rabin 2003, 2005, 2007) to correct the distortion in the consumption of a harmful good when consumers suffer from varying degrees of self-control problems. We take into account the possibility that consumers may trade the sin good in a secondary market, and show that sin licenses induce only sophisticated individuals with low levels of self-control problems to consume optimally. The consumption of naive individuals as well as sophisticated individuals with severe self-control problems remains too high, and welfare in equilibrium is decreasing in the level of self-control problems and non-increasing in the level of naivete. Further, we show that introducing a uniform tax on top of a system of sin licenses may improve welfare, whereas a uniform maximum quota would reduce welfare for sophisticates but may increase welfare for naives. Finally, we show that naives would benefit from a scheme where sin licenses are sold for a positive price in the primary market.